Chain in a maths lesson

Chain fits a maths lesson because it is short, it is the same puzzle for everyone that day, and it is not an arithmetic drill wearing a hat — the sums are the easy part and the reasoning is the point. It works best as a five-minute starter on a projector, with the class arguing about which tile to play. Below is how we would run it, including one lesson written out minute by minute. The rules take two minutes to read, and it is worth playing two or three yourself before you put one in front of thirty people.

What the puzzle actually asks

The board gives a start number, a target, and a small hand of tiles. You reach the target from the start in exactly the number of moves shown, using each tile at most once. Tiles are +n, −n, ×n, ÷n (only when the division comes out whole) and swap digits, which reverses the digits of the running value. Exactly one set of tiles solves the puzzle, and usually several orders of that set work, so two students with different orders can both be right — which is a more useful classroom fact than it sounds.

Difficulty follows the weekday and is the same for everyone: Monday and Tuesday are three moves, Wednesday, Thursday and Sunday are four, Friday and Saturday are five and are genuinely hard. For a starter with a mixed class, use a Monday or Tuesday board. Four moves is a reasonable whole-lesson discussion for a confident group.

As a five-minute starter

The shape that works: board on the screen before the students are in, no talking for the first minute, then hands.

The single rule worth imposing is that nobody says a whole solution. Suggestions are one tile at a time — "multiply by five" — and you play it, so the running value on the screen is the class's shared working. A student who has seen the answer stays useful, because they still have to persuade everyone else one move at a time, and that is harder and better than being first.

Undo and reset cost nothing, and a tile that cannot legally be played is simply refused with a reason on the screen. So a wrong suggestion is cheap and you should take it — play it, let the class see where it lands, undo it. The only thing that costs anything is playing the full number of moves and missing, which the board records as a try. Naming that at the start ("we are allowed to be wrong, it costs us a number on the screen and nothing else") gets more hands up than any amount of encouragement.

A starter, minute by minute

This is the real puzzle from Wednesday 9 September 2026: start 14, target 178, four moves, hand +89 +12 +17 ×5 +79.

Minute 0. Board up. Read it aloud: start fourteen, target one hundred and seventy-eight, four moves. One minute of silence, no hands, everyone thinking. Ask them to hold one first move in their head.

Minute 1. One question before any tile is played: how far apart are the start and the target? 178 − 14 = 164. Now a second: can the additions alone do it? Add the four addition tiles up as a class — 89 + 12 + 17 + 79 = 197. So 14 + 197 = 211, and that uses all four additions, which is exactly four moves. It lands on 211, not 178. That single piece of arithmetic proves the ×5 tile must be in the answer, before anybody has guessed anything. This is the moment worth the whole starter, and it is worth saying so.

Minute 2. Take a first tile from the class. If somebody says +89, play it: the board goes to 103, and now three tiles must produce 75 more, with a ×5 that would take 103 to 515. Let them see it, then undo. If somebody says ×5, play it: 14 becomes 70.

Minute 3. From 70, the hand is +89 +12 +17 +79 and three of them must make 108. Ask for the pair that gets close to a round number. 70 + 17 = 87, 87 + 12 = 99. Somebody will notice that 99 is one short of a hundred, and 99 + 79 is a bridging-through-100 sum that is genuinely worth practising out loud: 99 + 79 = 178.

Minute 4. Solved, in four moves: ×5 to 70, +17 to 87, +12 to 99, +79 to 178. Then the useful last thirty seconds — play the near miss. ×5 +89 +12 +17 gives 70, 159, 171, 188. Ten away, four moves used, and it is a miss. Close does not count here, which is the difference between a puzzle and an estimate.

The arithmetic it drills

Every board is two or three minutes of mental arithmetic that students choose to do because they want the answer to something else. On this one puzzle the class does 178 − 14, a four-number column addition, 14 × 5, three two-digit additions including one that bridges a hundred, and a division check. Nobody wrote a worksheet heading first.

The ÷n tile adds divisibility reasoning at no extra cost, because a division tile can only be played when it comes out whole. Hard days often turn on exactly that: the division has to go somewhere in the chain where the running value is divisible, and finding that position is a divisibility problem in disguise.

Working backwards from the target

This is the part that transfers, and it is worth teaching explicitly rather than letting students find it. Instead of asking what to do next, ask what the board must have looked like one move before the end. For each tile: for +n it is target − n, for −n it is target + n, for ×n it is target ÷ n and only if that comes out whole, for ÷n it is target × n.

Do it on the same puzzle and it collapses fast. Working back from 178: +79 needs 99, +17 needs 161, +12 needs 166, +89 needs 89, and ×5 needs 35.6 — not a whole number, so ×5 is not the last move. That is one line of arithmetic that removes a tile from consideration. Take 99 and go again: +12 needs 87, +17 needs 82, +89 needs 10. Take 87: +17 needs 70, and 70 is 14 × 5, which is the start. The whole chain, found backwards, without a single guess.

Undoing an operation to find its input is the same move students need for solving equations, for inverse functions later, and for checking any answer they have written down. Here it is the fastest way to win, which is a better argument for it than a teacher saying it is important. The strategy guide has more of these, including reading the last digit of the target to rule sets in and out.

Running it as a whole-class discussion

For fifteen or twenty minutes rather than five, change one thing: stop playing tiles and start writing on the whiteboard next to the projector. Keep the board frozen at the start position and build the argument in writing — the four additions total 197, so ×5 is in; ×5 cannot be last because 178 does not divide by 5; therefore ×5 is first or second. The class is now proving something rather than searching, and the board is only there to check the answer at the end.

Pairs work well for the middle of that: two minutes with the numbers copied into books, then take the reasoning rather than the answer. "What have you ruled out?" is a better question than "what did you get", and it gives students who have not finished something to say.

Use the archive so everyone has the same board

Today's puzzle is the same for every visitor, which is already useful — students who play at home will have had the same board as each other. But for a lesson you usually want a puzzle you have solved yourself first, and one that suits the group rather than whatever today happens to be.

That is what the archive is for: every finished day, newest first, each one replayable. Pick a puzzle from a few days back and you also get the solver's written walkthrough on that day's page, which appears once the day is old enough that nothing can be spoiled for anyone still playing. So the preparation is: open the archive a day or two ahead, find a Monday if you want three moves or a Wednesday if you want four, solve it yourself, read the walkthrough, and keep the page open in a tab. Every student who opens the same link sees the same board.

The archive also gives you a graceful exit if the starter dies on its feet. Drop to a three-move day and finish the five minutes on something the class actually solves.

Free, no sign-in, nothing to install

It matters in a classroom, so: playing costs nothing, there is no account to create, and nothing to install. Students do not hand over an email address to open a puzzle, and there is no class code, no roster, and no dashboard for you to set up before a lesson — and equally, nothing that reports back to you on who solved what, so this is a starter rather than an assessment. Progress is kept in the browser on that device, so a school machine that wipes between sessions simply starts fresh. An account exists for people who want their own streak on their phone and their laptop, and it is entirely optional; a lesson never needs one.

The board works from a keyboard alone, which is worth knowing if you are driving it from the front: number keys 1 to 6 play tiles by position and Backspace undoes, so you can run the whole starter without reaching for a mouse.

If a puzzle looks wrong, or you want a difficulty we do not currently produce, the feedback button on any page reaches us directly. The FAQ covers when the day rolls over and what the site stores.